Abstract
In the study of transport in inhomogeneous systems it is common to
construct transport equations invoking the inhomogeneous Fick
law. The validity of this approach requires that at least two
ingredients be present in the system. First, finite characteristic
length and time scales associated to the dominant transport
process must exist. Secondly, the transport mechanism must satisfy
a microscopic symmetry: global reversibility. Global reversibility
is often satisfied in nature. However, many complex systems
exhibit a lack of finite characteristic scales. In this Letter we
show how to construct a generalization of the inhomogeneous Fick
law that does not require the existence of characteristic scales
while still satisfying global reversibility.